A Stability and Accuracy Validation Method for Multirate Digital Simulation
Bibliographic record
Abstract
This paper presents a new validation method to demonstrate the stability and accuracy of a discretized system by using multiple sampling rates. Such multirate simulations are often encountered in real-time simulation application, where large power systems are coupled with circuit containing power electronics devices. Multirate simulation should not be confused with variable-step simulation, which is a single-rate simulation type. In single-rate simulation, the discretized system is stable when its discrete poles are within the unitary circle. When using multirate solvers, state variables are discretized with different sampling rates and poles location analysis for the system's equations cannot be used. This paper introduces a formal mathematical analysis demonstrating stability of multirate real-time simulation. System state variables, regardless of their discretization time step, are found in a single matrix. Classical pole analyses are thereafter used to test stability with poles location analysis. The method is given in a generalized form, and can be applied to various multirate solvers. The proposed method was found accurate and reliable using numerical examples.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".